Are two opposite rays with common endpoint considered to have an angle? Why?

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Yes. Any two rays joined with an endpoint always have, by definition, an angle between them. Two opposite rays form a straight line. The angle of a straight line is 180 degrees. To see this, imagine that one ray is tilted slightly up or down from being exactly a straight line. Then the angle between the rays would be about 179 degrees, or 181 degrees.

Even two rays joined with an endpoint and pointing in the same direction have an angle between them: it is 360 degrees (or 0 degrees).

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